Trabalho Estatistica
Equipe:
Carlos Alberto Figueiredo - RM330568
Daiana Cristina Zanelli Mota - RM330722
Diogo Silva Rocha - RM330717
Renato Belandrino Rodrigues - RM330579
install.packages(“psych”) install.packages(“plotly”) install.packages(“gmodels”) install.packages(“corrgram”)
# mostrar atÈ 2 casas decimais
options("scipen" = 2)
# Ler arquivo csv
Vinhos <- read.csv2("BaseWineRedeWhite2018.csv", row.names=1)#Vinhos <- BaseWine_Red_e_White2018
#fix(Vinhos)
#mostrar as vari·veis
#str(Vinhos)
#mostra as vari·veis
names(Vinhos)## [1] "fixedacidity" "volatileacidity" "citricacid"
## [4] "residualsugar" "chlorides" "freesulfurdioxide"
## [7] "totalsulfurdioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
## [13] "Vinho"#XX Variáveis e muita informaçãoattach(Vinhos)
# FrequÍncia absoluta
table(as.factor(Vinhos$quality), Vinhos$Vinho, useNA = "ifany")##
## RED WHITE
## 3 10 20
## 4 53 163
## 5 681 1457
## 6 638 2198
## 7 199 880
## 8 18 175
## 9 0 5table(as.factor(Vinhos$quality), Vinhos$Vinho)##
## RED WHITE
## 3 10 20
## 4 53 163
## 5 681 1457
## 6 638 2198
## 7 199 880
## 8 18 175
## 9 0 5Análise:
Avaliando as duas tabelas de frequência das notas/qualiade que comparam os vinhos tintos e brancos, vemos que não exsitem valores “brancos/NA” já que as duas tabelas apresentam as mesmas frequências.
Olhando os valores entre as duas tabelas, testamos a hipótese da resposta de qualidade ser diverente entre os vinhos Brancos e Tintos. Para isso fizemos um Teste para duas amostras
Quality <- split(Vinhos, Vinhos$Vinho)
t.test(Quality$WHITE$quality, Quality$RED$quality)##
## Welch Two Sample t-test
##
## data: Quality$WHITE$quality and Quality$RED$quality
## t = 10.149, df = 2950.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.1951564 0.2886173
## sample estimates:
## mean of x mean of y
## 5.877909 5.636023Análise:
A partir do valor do p-value e risco alfa máximo de 5%, podemos dizer que os vinhos Brancos e Tintos tem valores médios de notas diferentes, já que o p-value < 2.2e-16
# 2-Way Cross Tabulation
library(gmodels)## Warning: package 'gmodels' was built under R version 3.4.4CrossTable(as.factor(Vinhos$quality), Vinhos$Vinho) ##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 6497
##
##
## | Vinhos$Vinho
## as.factor(Vinhos$quality) | RED | WHITE | Row Total |
## --------------------------|-----------|-----------|-----------|
## 3 | 10 | 20 | 30 |
## | 0.927 | 0.303 | |
## | 0.333 | 0.667 | 0.005 |
## | 0.006 | 0.004 | |
## | 0.002 | 0.003 | |
## --------------------------|-----------|-----------|-----------|
## 4 | 53 | 163 | 216 |
## | 0.000 | 0.000 | |
## | 0.245 | 0.755 | 0.033 |
## | 0.033 | 0.033 | |
## | 0.008 | 0.025 | |
## --------------------------|-----------|-----------|-----------|
## 5 | 681 | 1457 | 2138 |
## | 45.546 | 14.869 | |
## | 0.319 | 0.681 | 0.329 |
## | 0.426 | 0.297 | |
## | 0.105 | 0.224 | |
## --------------------------|-----------|-----------|-----------|
## 6 | 638 | 2198 | 2836 |
## | 5.154 | 1.683 | |
## | 0.225 | 0.775 | 0.437 |
## | 0.399 | 0.449 | |
## | 0.098 | 0.338 | |
## --------------------------|-----------|-----------|-----------|
## 7 | 199 | 880 | 1079 |
## | 16.681 | 5.446 | |
## | 0.184 | 0.816 | 0.166 |
## | 0.124 | 0.180 | |
## | 0.031 | 0.135 | |
## --------------------------|-----------|-----------|-----------|
## 8 | 18 | 175 | 193 |
## | 18.321 | 5.981 | |
## | 0.093 | 0.907 | 0.030 |
## | 0.011 | 0.036 | |
## | 0.003 | 0.027 | |
## --------------------------|-----------|-----------|-----------|
## 9 | 0 | 5 | 5 |
## | 1.231 | 0.402 | |
## | 0.000 | 1.000 | 0.001 |
## | 0.000 | 0.001 | |
## | 0.000 | 0.001 | |
## --------------------------|-----------|-----------|-----------|
## Column Total | 1599 | 4898 | 6497 |
## | 0.246 | 0.754 | |
## --------------------------|-----------|-----------|-----------|
##
## Análise:
A partir da tabela cruzada entre tipo do vinho (Branco e Tinto) e as notas de qualidade, podemos perceber a maior frequencia geral é de notas 6 (43,7%).
Mas olhando para cada tipo de vinho individualmente, a nota 6 é mais frequente para o vinho branco(44,9%), enquanto a nota mais frenquente para o vinho tinto é 5 (42,6%), o que ajuda a confirmar a diferença entre os vinhos, com relação as notas de qualidade.
summary(Vinhos)## fixedacidity volatileacidity citricacid residualsugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.60
## 1st Qu.: 6.400 1st Qu.:0.2300 1st Qu.:0.2500 1st Qu.: 1.80
## Median : 7.000 Median :0.2900 Median :0.3100 Median : 3.00
## Mean : 7.215 Mean :0.3397 Mean :0.3186 Mean : 5.44
## 3rd Qu.: 7.700 3rd Qu.:0.4000 3rd Qu.:0.3900 3rd Qu.: 8.10
## Max. :15.900 Max. :1.5800 Max. :1.6600 Max. :45.80
## chlorides freesulfurdioxide totalsulfurdioxide density
## Min. :0.00900 Min. : 1.00 Min. : 6.0 Min. :0.9871
## 1st Qu.:0.03800 1st Qu.: 17.00 1st Qu.: 77.0 1st Qu.:0.9923
## Median :0.04700 Median : 29.00 Median :118.0 Median :0.9949
## Mean :0.05603 Mean : 30.53 Mean :115.7 Mean :0.9947
## 3rd Qu.:0.06500 3rd Qu.: 41.00 3rd Qu.:156.0 3rd Qu.:0.9970
## Max. :0.61100 Max. :289.00 Max. :440.0 Max. :1.0140
## pH sulphates alcohol quality
## Min. :2.720 Min. :0.2200 Min. : 0.9567 Min. :3.000
## 1st Qu.:3.110 1st Qu.:0.4300 1st Qu.: 9.5000 1st Qu.:5.000
## Median :3.210 Median :0.5100 Median :10.3000 Median :6.000
## Mean :3.219 Mean :0.5313 Mean :10.4862 Mean :5.818
## 3rd Qu.:3.320 3rd Qu.:0.6000 3rd Qu.:11.3000 3rd Qu.:6.000
## Max. :4.010 Max. :2.0000 Max. :14.9000 Max. :9.000
## Vinho
## RED :1599
## WHITE:4898
##
##
##
## Análise:
Olhando as estatísticas básicas de todas as proprieddes, podemos perceber alguns pontos:
Médias próximas as medianas, que indica possível simetria nas distribuições para: fixedacidity, volatileacidity, citricacid, chlorides, freesulfurdioxide, totalsulfurdioxide, density, pH, sulphates, alcohol e quality.
Avaliando os valores máximos e mínimos, temos indícios de outliers para: citricacid (mínimo e máximo), residualsugar (máximo), chloride (máximo), freesulfurdioxide (máximo), sulphates (máximo).
aggregate (Vinhos,
by = list(Vinho),
FUN = "mean")## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA## Group.1 fixedacidity volatileacidity citricacid residualsugar chlorides
## 1 RED 8.319637 0.5278205 0.2709756 2.538806 0.08746654
## 2 WHITE 6.854788 0.2782411 0.3341915 6.387332 0.04577236
## freesulfurdioxide totalsulfurdioxide density pH sulphates
## 1 15.87492 46.46779 0.9967467 3.311113 0.6581488
## 2 35.30808 138.36066 0.9940223 3.188267 0.4898469
## alcohol quality Vinho
## 1 10.40008 5.636023 NA
## 2 10.51427 5.877909 NAAnálise:
Função retorna a media de todas as vaiáveis numéricas para os vinhos Brancos e Tintos Pontos que chamam a atenção:
residualsugar é muito maior para os brancos apesar do alcohol ter valores próximos.
freesulfurdioxide e totalsulfurdioxide é maior nos vinhos brancos que nos tintos. Este conservante também serve para previnir o escurecimento dos vinhos. Por isso, talvez, sua maior concentração nos Brancos.
O cometário “argument is not numeric or logical: returning NAargument is not numeric or logical: returning NA” é devido a variável vinho que não é numérica
mean(Vinhos$fixedacidity) # mÈdia## [1] 7.215307median(Vinhos$fixedacidity) # mÈdiana## [1] 7quantile(Vinhos$fixedacidity,type=4) # Quartis## 0% 25% 50% 75% 100%
## 3.8 6.4 7.0 7.7 15.9quantile(Vinhos$fixedacidity,.65,type=4) # exato percentil## 65%
## 7.3range(Vinhos$fixedacidity) # amplitude## [1] 3.8 15.9diff(range(Vinhos$fixedacidity)) #diferenÁa entre o maior e o menor valor## [1] 12.1min(Vinhos$fixedacidity) # valor mÌnimo de x## [1] 3.8max(Vinhos$fixedacidity) # valor m·ximo de x## [1] 15.9var(Vinhos$fixedacidity) # para obter a vari‚ncia## [1] 1.68074sd(Vinhos$fixedacidity) # para obter o desvio padr„o## [1] 1.296434CV_fixedacidity<-sd(Vinhos$fixedacidity)/mean(Vinhos$fixedacidity)*100 # para obter o coefiiente de variaÁ„o
CV_fixedacidity## [1] 17.96783Análise:
As funções retornam estaísticas decritivas para a variavel fixedacidity, inclusive o Coeficiente de Variação (CV).
CV = Em teoria das probabilidades e estatística, o coeficiente de variação (CV), também conhecido como desvio padrão relativo (DPR), é uma medida padronizada de dispersão de uma distribuição de probabilidade ou de uma distribuição de frequências. É frequentemente expresso como uma porcentagem, sendo definido como a razão do desvio padrão pela média (ou seu valor absoluto. O CV ou DPR é amplamente usado em química analítica para expressar a precisão e a repetitividade de um ensaio. Também é comumente usado em campos como engenharia e física quando se fazem estudos de garantia de qualidade e avaliações de repetitividade e reprodutibilidade. O CV também é usado por economistas e investidores em modelos econômicos e na determinação da volatilidade de um valor mobiliário. Fonte: Wikipédia
#comando para gerar em 3 linhas e 4 colunas os histogramas
par (mfrow=c(3,4))
hist(fixedacidity)
hist(volatileacidity)
hist(citricacid )
hist(residualsugar)
hist(chlorides)
hist(freesulfurdioxide)
hist(totalsulfurdioxide)
hist(density)
hist(pH)
hist(sulphates)
hist(alcohol)
hist(quality)
Análise:
Avaliando os histogrmas, alguns pontos chamam a atenção:
As escalas estão bem abertas, indicando a presença de Outliers, principalmente para: volatileacidity, citricacid, chlorides, freesulfurdioxide
Distribuições assimetricas, com mínimos limitados pelo valor zero, por exemplo: volatileacidity, residualsugar, chlorides, freesulfurdioxide
hist(quality, col=c("pink"), col.main="darkgray", prob=T)
Análise:
- O histograma da quality, por ter valores inteiros, o histograma parece “dentado” mas que não invalida a análise de uma distribuição simétrica, possivelmente Normal
attach(Vinhos)## The following objects are masked from Vinhos (pos = 4):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity#comando para gerar em 3 linhas e 4 colunas os histogramas
par (mfrow=c(3,4))
boxplot(fixedacidity, main='fixedacidity')
boxplot(volatileacidity , main='volatileacidity')
boxplot(citricacid , main='citricacid')
boxplot(residualsugar, main='residualsugar')
boxplot(chlorides, main='chlorides')
boxplot(freesulfurdioxide, main='freesulfurdioxide')
boxplot(totalsulfurdioxide, main='totalsulfurdioxide')
boxplot(density, main='density')
boxplot(pH, main='pH')
boxplot(sulphates, main='sulphates')
boxplot(alcohol, main='alcohol')
boxplot(Vinhos$quality, main='quality')
Análise:
As análises dos Box Plots validam as que já fizemos para os histogramas.
Apesar de todos os Box Plots apresentarem Outliers, que pode ser efeito dos tamanhos de amostra, os BoxPlots com maiores quantidade de outliers são: volatileacidity, citricacid, chlorides, freesulfurdioxide. citricacid, freesulfurdioxide e alcohol com valores pontuais bem distantes da distribuição. Valeria uma melhor avaliação destes pontos de medidas para verificação se realmente são pontos fora da curva esperada.
Distribuições assimetricas, com principal atenção para residualsugar, onde a assimentria se destaca na forma da caixa de dos bigodes do Box Plot. Mediana deslocada para o Q1 e bigode inferior bem menor que o superior.
boxplot(quality ~ Vinho, main='quality')
boxplot(fixedacidity ~ Vinho, main='fixedacidity',col=c('red','blue'))
boxplot(volatileacidity ~ Vinho , main='volatileacidity')
boxplot(citricacid ~ Vinho, main='citricacid')
boxplot(residualsugar ~ Vinho, main='residualsugar',col=c('red','blue'))
boxplot(chlorides ~ Vinho, main='chlorides')
boxplot(freesulfurdioxide ~ Vinho, main='freesulfurdioxide')
boxplot(totalsulfurdioxide ~ Vinho, main='totalsulfurdioxide')
boxplot(density ~ Vinho, main='density')
boxplot(pH ~ Vinho, main='pH')
boxplot(sulphates ~ Vinho, main='sulphates')
boxplot(alcohol ~ Vinho, main='alcohol')
Análise:
Os Box Plots para todas as características, agora comparando os vinhos brancos e tintos podem servir para entender características que podem distinguir entre estes dois tipos e vinhos, como já fizemos com a quality, usando o teste de hipótese.
Olhando os Box Plots, outras características que podem ser diferentes por tipo de vinho são: volatileacidity, chlorides, freesulfurdioxide e totalsulfurdioxide (já comentado nas estatísticas descritivas)
# Gr·fico de dispers„o ( pch=caracter, lwd=largura)
plot(freesulfurdioxide~totalsulfurdioxide)
plot(freesulfurdioxide~totalsulfurdioxide, pch=1, lwd=3)
plot(freesulfurdioxide~totalsulfurdioxide)
abline(h=mean(freesulfurdioxide), col="red")
abline(v=mean(totalsulfurdioxide), col="green")
Análise:
O Gráfico de dispersão mostra a relação de previsão entre as variáveis. Neste caso entre freesulfurdioxide e totalsulfurdioxide.
Estas variáveis aparentam ter uma correlação forte (núvem de pontos com pouca dispersão) e positiva (inclinação positiva/coeficiente angular > 0), indicando que a partir da informação sobre totalsulfurdioxide pode prever o valor de freesulfurdioxide, com boa acuracidade.
A linha verde representa a média do totalsulfurdioxide e a vermelha a média do freesulfurdioxide. O ponto onde onde as retas se encontram é um dos pontos que fará parte da regressão linear entre as variáveis e da uma ideia de centramento desta relação
attach(Vinhos)## The following objects are masked from Vinhos (pos = 3):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity## The following objects are masked from Vinhos (pos = 5):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidityVinhos$fx_redSugar <- cut(residualsugar,breaks=c(0,10,20,30,max(residualsugar)))
Vinhos$fx_redSugar ## [1] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [7] (0,10] (0,10] (0,10] (20,30] (0,10] (0,10]
## [13] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [19] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [25] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [31] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [37] (0,10] (0,10] (0,10] (10,20] (10,20] (20,30]
## [43] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [49] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [55] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [61] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [67] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [73] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [79] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [85] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [91] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [97] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [103] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [109] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [115] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [121] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [127] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [133] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [139] (0,10] (10,20] (0,10] (10,20] (0,10] (10,20]
## [145] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [151] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [157] (10,20] (10,20] (0,10] (10,20] (10,20] (0,10]
## [163] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [169] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [175] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [181] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [187] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [193] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [199] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [205] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [211] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [217] (10,20] (0,10] (0,10] (20,30] (10,20] (10,20]
## [223] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [229] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [235] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [241] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [247] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [253] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [259] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [265] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [271] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [277] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [283] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [289] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [295] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [301] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [307] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [313] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [319] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [325] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [331] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [337] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [343] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [349] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [355] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [361] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [367] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [373] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [379] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [385] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [391] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [397] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [403] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [409] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [415] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [421] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [427] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [433] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [439] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [445] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [451] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [457] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [463] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [469] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [475] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [481] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [487] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [493] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [499] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [505] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [511] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [517] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [523] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [529] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [535] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [541] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [547] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [553] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [559] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [565] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [571] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [577] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [583] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [589] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [595] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [601] (0,10] (0,10] (20,30] (10,20] (0,10] (0,10]
## [607] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [613] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [619] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [625] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [631] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [637] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [643] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [649] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [655] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [661] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [667] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [673] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [679] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [685] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [691] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [697] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [703] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [709] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [715] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [721] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [727] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [733] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [739] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [745] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [751] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [757] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [763] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [769] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [775] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [781] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [787] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [793] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [799] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [805] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [811] (0,10] (10,20] (10,20] (0,10] (10,20] (10,20]
## [817] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [823] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [829] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [835] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [841] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [847] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [853] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [859] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [865] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [871] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [877] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [883] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [889] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [895] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [901] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [907] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [913] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [919] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [925] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [931] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [937] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [943] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [949] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [955] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [961] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [967] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [973] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [979] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [985] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [991] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [997] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1003] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1009] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1015] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1021] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1027] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1033] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [1039] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1045] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1051] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1057] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1063] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1069] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1075] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1081] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1087] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1093] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1099] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1105] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [1111] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1117] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1123] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1129] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [1135] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1141] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1147] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1153] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1159] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1165] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1171] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1177] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1183] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1189] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1195] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1201] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1207] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [1213] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1219] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [1225] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [1231] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1237] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [1243] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1249] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1255] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1261] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1267] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1273] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1279] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1285] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1291] (0,10] (0,10] (0,10] (10,20] (10,20] (10,20]
## [1297] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1303] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1309] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1315] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [1321] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1327] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1333] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1339] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1345] (10,20] (10,20] (0,10] (10,20] (0,10] (0,10]
## [1351] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1357] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1363] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1369] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1375] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1381] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1387] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1393] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1399] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1405] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1411] (10,20] (10,20] (0,10] (10,20] (0,10] (0,10]
## [1417] (0,10] (10,20] (0,10] (0,10] (0,10] (20,30]
## [1423] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1429] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1435] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1441] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1447] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [1453] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1459] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1465] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1471] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1477] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [1483] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1489] (0,10] (10,20] (20,30] (0,10] (0,10] (0,10]
## [1495] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1501] (0,10] (0,10] (10,20] (0,10] (30,45.8] (0,10]
## [1507] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1513] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1519] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1525] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1531] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1537] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1543] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1549] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [1555] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1561] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1567] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1573] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1579] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1585] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1591] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1597] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1603] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1609] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1615] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1621] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1627] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1633] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1639] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1645] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1651] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1657] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1663] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1669] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1675] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [1681] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1687] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1693] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1699] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1705] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1711] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1717] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1723] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1729] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1735] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1741] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1747] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1753] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1759] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1765] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [1771] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1777] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1783] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [1789] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1795] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1801] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1807] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1813] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [1819] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1825] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [1831] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1837] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1843] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [1849] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1855] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [1861] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1867] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1873] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1879] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1885] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1891] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [1897] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1903] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1909] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [1915] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1921] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1927] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1933] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1939] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1945] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [1951] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [1957] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [1963] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [1969] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [1975] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [1981] (0,10] (0,10] (0,10] (0,10] (0,10] (20,30]
## [1987] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [1993] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [1999] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2005] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2011] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2017] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2023] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2029] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2035] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2041] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2047] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2053] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2059] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2065] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2071] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2077] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2083] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2089] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2095] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2101] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2107] (10,20] (10,20] (10,20] (0,10] (0,10] (10,20]
## [2113] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [2119] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2125] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2131] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2137] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2143] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2149] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2155] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [2161] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2167] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2173] (0,10] (10,20] (0,10] (10,20] (0,10] (10,20]
## [2179] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2185] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2191] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2197] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2203] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2209] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2215] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2221] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2227] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2233] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2239] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2245] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2251] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2257] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2263] (0,10] (0,10] (10,20] (0,10] (10,20] (10,20]
## [2269] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2275] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2281] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2287] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2293] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2299] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2305] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2311] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2317] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2323] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [2329] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2335] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [2341] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2347] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2353] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2359] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2365] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2371] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2377] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2383] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [2389] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2395] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2401] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2407] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [2413] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2419] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2425] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2431] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2437] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [2443] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2449] (10,20] (10,20] (0,10] (10,20] (10,20] (0,10]
## [2455] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2461] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2467] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [2473] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2479] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2485] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2491] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2497] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2503] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2509] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2515] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2521] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2527] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2533] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2539] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2545] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2551] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2557] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2563] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2569] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2575] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2581] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2587] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2593] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2599] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2605] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2611] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2617] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2623] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [2629] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [2635] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2641] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2647] (0,10] (20,30] (0,10] (0,10] (0,10] (0,10]
## [2653] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2659] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2665] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2671] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2677] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [2683] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2689] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2695] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2701] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2707] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2713] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2719] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2725] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [2731] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [2737] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2743] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2749] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2755] (10,20] (10,20] (10,20] (10,20] (0,10] (0,10]
## [2761] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [2767] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2773] (0,10] (10,20] (10,20] (0,10] (10,20] (0,10]
## [2779] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2785] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2791] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2797] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2803] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2809] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2815] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2821] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [2827] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2833] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2839] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2845] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [2851] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2857] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2863] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2869] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2875] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2881] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2887] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2893] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [2899] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [2905] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [2911] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [2917] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2923] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [2929] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [2935] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [2941] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2947] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [2953] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2959] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [2965] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2971] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [2977] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2983] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [2989] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [2995] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3001] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3007] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3013] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3019] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3025] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3031] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3037] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3043] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3049] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3055] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3061] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3067] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3073] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3079] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3085] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3091] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3097] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3103] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3109] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3115] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3121] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3127] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3133] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3139] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3145] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3151] (0,10] (0,10] (0,10] (0,10] (0,10] (20,30]
## [3157] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3163] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3169] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3175] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3181] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3187] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3193] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3199] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3205] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3211] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3217] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3223] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3229] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3235] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3241] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3247] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3253] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3259] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3265] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3271] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3277] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3283] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3289] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3295] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3301] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3307] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3313] (10,20] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3319] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3325] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3331] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3337] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3343] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3349] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3355] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3361] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3367] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3373] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3379] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3385] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3391] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3397] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3403] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3409] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3415] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3421] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [3427] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3433] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3439] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3445] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3451] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3457] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3463] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3469] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3475] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3481] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3487] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3493] (0,10] (10,20] (10,20] (0,10] (10,20] (0,10]
## [3499] (10,20] (0,10] (10,20] (10,20] (10,20] (0,10]
## [3505] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3511] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3517] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3523] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3529] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3535] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3541] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3547] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3553] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [3559] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3565] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3571] (0,10] (30,45.8] (0,10] (0,10] (0,10] (0,10]
## [3577] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3583] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3589] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3595] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3601] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3607] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3613] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3619] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [3625] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [3631] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3637] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3643] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3649] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3655] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3661] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [3667] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3673] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3679] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3685] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3691] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3697] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3703] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3709] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3715] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3721] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3727] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3733] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3739] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3745] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3751] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [3757] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3763] (0,10] (10,20] (0,10] (0,10] (10,20] (10,20]
## [3769] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3775] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [3781] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3787] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3793] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [3799] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3805] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3811] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3817] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3823] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [3829] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3835] (0,10] (0,10] (0,10] (0,10] (0,10] (30,45.8]
## [3841] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [3847] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3853] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3859] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3865] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [3871] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3877] (10,20] (0,10] (10,20] (10,20] (0,10] (0,10]
## [3883] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [3889] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [3895] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3901] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [3907] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3913] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3919] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3925] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3931] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [3937] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3943] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3949] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3955] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3961] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3967] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3973] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [3979] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3985] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [3991] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [3997] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4003] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4009] (10,20] (0,10] (10,20] (0,10] (10,20] (10,20]
## [4015] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4021] (0,10] (10,20] (20,30] (0,10] (10,20] (10,20]
## [4027] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4033] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4039] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4045] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4051] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4057] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4063] (10,20] (0,10] (0,10] (10,20] (10,20] (0,10]
## [4069] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4075] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4081] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4087] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4093] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4099] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4105] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4111] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4117] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4123] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4129] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4135] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [4141] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4147] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4153] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4159] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4165] (0,10] (10,20] (10,20] (10,20] (0,10] (10,20]
## [4171] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4177] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4183] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4189] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4195] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4201] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4207] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4213] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4219] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4225] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4231] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [4237] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4243] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4249] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4255] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4261] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4267] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4273] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4279] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4285] (10,20] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4291] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4297] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4303] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4309] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4315] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4321] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4327] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4333] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [4339] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4345] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [4351] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4357] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4363] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4369] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4375] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4381] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4387] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4393] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4399] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4405] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4411] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4417] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4423] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4429] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4435] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4441] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [4447] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4453] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4459] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4465] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4471] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4477] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4483] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4489] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4495] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4501] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4507] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4513] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4519] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4525] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4531] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4537] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4543] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4549] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4555] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4561] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4567] (0,10] (10,20] (10,20] (0,10] (10,20] (0,10]
## [4573] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4579] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4585] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [4591] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4597] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4603] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4609] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4615] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4621] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4627] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4633] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4639] (10,20] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4645] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4651] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4657] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4663] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4669] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [4675] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4681] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4687] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4693] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4699] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4705] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4711] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4717] (0,10] (10,20] (10,20] (0,10] (0,10] (10,20]
## [4723] (10,20] (10,20] (0,10] (0,10] (10,20] (10,20]
## [4729] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4735] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4741] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4747] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4753] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4759] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4765] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4771] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [4777] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4783] (10,20] (0,10] (10,20] (10,20] (10,20] (0,10]
## [4789] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4795] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4801] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4807] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [4813] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [4819] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4825] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [4831] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [4837] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4843] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4849] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4855] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [4861] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4867] (0,10] (10,20] (0,10] (10,20] (0,10] (0,10]
## [4873] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4879] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4885] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4891] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4897] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4903] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4909] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4915] (10,20] (10,20] (0,10] (0,10] (0,10] (20,30]
## [4921] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4927] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [4933] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [4939] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [4945] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [4951] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [4957] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [4963] (0,10] (20,30] (10,20] (10,20] (10,20] (0,10]
## [4969] (10,20] (0,10] (10,20] (0,10] (0,10] (10,20]
## [4975] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4981] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [4987] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4993] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [4999] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5005] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5011] (10,20] (10,20] (10,20] (10,20] (0,10] (0,10]
## [5017] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5023] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5029] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5035] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5041] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5047] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5053] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5059] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5065] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5071] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5077] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5083] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5089] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5095] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [5101] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5107] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5113] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5119] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5125] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5131] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5137] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5143] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5149] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5155] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5161] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5167] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5173] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5179] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5185] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5191] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5197] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5203] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5209] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5215] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5221] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5227] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5233] (0,10] (0,10] (20,30] (0,10] (0,10] (0,10]
## [5239] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5245] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5251] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5257] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5263] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [5269] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5275] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5281] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5287] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [5293] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5299] (10,20] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5305] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5311] (0,10] (10,20] (0,10] (0,10] (0,10] (10,20]
## [5317] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [5323] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5329] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5335] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5341] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5347] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5353] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5359] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5365] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5371] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5377] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5383] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5389] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5395] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5401] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5407] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5413] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5419] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [5425] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5431] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5437] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5443] (0,10] (20,30] (0,10] (0,10] (0,10] (10,20]
## [5449] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5455] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [5461] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5467] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5473] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5479] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5485] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5491] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5497] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5503] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [5509] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5515] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5521] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5527] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5533] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5539] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5545] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5551] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5557] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5563] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5569] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5575] (10,20] (10,20] (0,10] (0,10] (0,10] (10,20]
## [5581] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5587] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5593] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5599] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5605] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5611] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5617] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5623] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5629] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5635] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5641] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5647] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5653] (20,30] (0,10] (10,20] (10,20] (10,20] (0,10]
## [5659] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5665] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5671] (0,10] (0,10] (10,20] (10,20] (0,10] (10,20]
## [5677] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5683] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5689] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5695] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5701] (10,20] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5707] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5713] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5719] (0,10] (0,10] (10,20] (0,10] (10,20] (10,20]
## [5725] (0,10] (10,20] (0,10] (10,20] (0,10] (10,20]
## [5731] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5737] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5743] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5749] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5755] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5761] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [5767] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5773] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5779] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5785] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5791] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [5797] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5803] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [5809] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5815] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5821] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5827] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5833] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5839] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [5845] (0,10] (0,10] (10,20] (10,20] (10,20] (0,10]
## [5851] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [5857] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5863] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5869] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5875] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5881] (0,10] (0,10] (10,20] (0,10] (10,20] (10,20]
## [5887] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [5893] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5899] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5905] (10,20] (0,10] (0,10] (10,20] (10,20] (10,20]
## [5911] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [5917] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [5923] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5929] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5935] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5941] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5947] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [5953] (0,10] (10,20] (0,10] (0,10] (10,20] (10,20]
## [5959] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5965] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [5971] (10,20] (0,10] (10,20] (10,20] (0,10] (0,10]
## [5977] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5983] (0,10] (0,10] (10,20] (0,10] (10,20] (0,10]
## [5989] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [5995] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6001] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6007] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6013] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [6019] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6025] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6031] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [6037] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6043] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6049] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [6055] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6061] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6067] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6073] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6079] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6085] (10,20] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6091] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6097] (10,20] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6103] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6109] (0,10] (10,20] (10,20] (0,10] (0,10] (0,10]
## [6115] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6121] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6127] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6133] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6139] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6145] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [6151] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6157] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6163] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6169] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6175] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6181] (10,20] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6187] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6193] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6199] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6205] (0,10] (10,20] (10,20] (10,20] (0,10] (0,10]
## [6211] (0,10] (0,10] (10,20] (10,20] (0,10] (0,10]
## [6217] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6223] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6229] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6235] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6241] (0,10] (10,20] (0,10] (0,10] (10,20] (0,10]
## [6247] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6253] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6259] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6265] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6271] (0,10] (0,10] (0,10] (0,10] (10,20] (10,20]
## [6277] (10,20] (0,10] (10,20] (0,10] (10,20] (0,10]
## [6283] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6289] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6295] (10,20] (0,10] (0,10] (10,20] (10,20] (10,20]
## [6301] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6307] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6313] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6319] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6325] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6331] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6337] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6343] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6349] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6355] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6361] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6367] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6373] (10,20] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6379] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6385] (0,10] (0,10] (0,10] (10,20] (10,20] (0,10]
## [6391] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6397] (0,10] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6403] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6409] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6415] (0,10] (0,10] (0,10] (0,10] (0,10] (10,20]
## [6421] (10,20] (10,20] (0,10] (0,10] (10,20] (0,10]
## [6427] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6433] (0,10] (0,10] (0,10] (0,10] (10,20] (0,10]
## [6439] (10,20] (0,10] (10,20] (0,10] (0,10] (0,10]
## [6445] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6451] (0,10] (0,10] (0,10] (10,20] (0,10] (0,10]
## [6457] (0,10] (0,10] (0,10] (10,20] (0,10] (10,20]
## [6463] (0,10] (10,20] (0,10] (0,10] (0,10] (0,10]
## [6469] (0,10] (0,10] (10,20] (0,10] (0,10] (10,20]
## [6475] (0,10] (10,20] (0,10] (10,20] (10,20] (0,10]
## [6481] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6487] (0,10] (0,10] (0,10] (0,10] (0,10] (0,10]
## [6493] (0,10] (0,10] (0,10] (0,10] (0,10]
## Levels: (0,10] (10,20] (20,30] (30,45.8]str(Vinhos)## 'data.frame': 6497 obs. of 14 variables:
## $ fixedacidity : num 6.6 6.7 10.6 5.4 6.7 6.8 6.6 7.2 5.1 6.2 ...
## $ volatileacidity : num 0.24 0.34 0.31 0.18 0.3 0.5 0.61 0.66 0.26 0.22 ...
## $ citricacid : num 0.35 0.43 0.49 0.24 0.44 0.11 0 0.33 0.33 0.2 ...
## $ residualsugar : num 7.7 1.6 2.2 4.8 18.8 ...
## $ chlorides : num 0.031 0.041 0.063 0.041 0.057 0.075 0.069 0.068 0.027 0.035 ...
## $ freesulfurdioxide : num 36 29 18 30 65 16 4 34 46 58 ...
## $ totalsulfurdioxide: num 135 114 40 113 224 49 8 102 113 184 ...
## $ density : num 0.994 0.99 0.998 0.994 1 ...
## $ pH : num 3.19 3.23 3.14 3.42 3.11 3.36 3.33 3.27 3.35 3.11 ...
## $ sulphates : num 0.37 0.44 0.51 0.4 0.53 0.79 0.37 0.78 0.43 0.53 ...
## $ alcohol : num 10.5 12.6 9.8 9.4 9.1 9.5 10.4 12.8 11.4 9 ...
## $ quality : int 5 6 6 6 5 5 4 6 7 6 ...
## $ Vinho : Factor w/ 2 levels "RED","WHITE": 2 2 1 2 2 1 1 1 2 2 ...
## $ fx_redSugar : Factor w/ 4 levels "(0,10]","(10,20]",..: 1 1 1 1 2 1 1 1 1 3 ...CrossTable( Vinhos$fx_redSugar , Vinhos$Vinho) ##
##
## Cell Contents
## |-------------------------|
## | N |
## | Chi-square contribution |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 6497
##
##
## | Vinhos$Vinho
## Vinhos$fx_redSugar | RED | WHITE | Row Total |
## -------------------|-----------|-----------|-----------|
## (0,10] | 1588 | 3705 | 5293 |
## | 62.493 | 20.401 | |
## | 0.300 | 0.700 | 0.815 |
## | 0.993 | 0.756 | |
## | 0.244 | 0.570 | |
## -------------------|-----------|-----------|-----------|
## (10,20] | 11 | 1175 | 1186 |
## | 270.305 | 88.244 | |
## | 0.009 | 0.991 | 0.183 |
## | 0.007 | 0.240 | |
## | 0.002 | 0.181 | |
## -------------------|-----------|-----------|-----------|
## (20,30] | 0 | 15 | 15 |
## | 3.692 | 1.205 | |
## | 0.000 | 1.000 | 0.002 |
## | 0.000 | 0.003 | |
## | 0.000 | 0.002 | |
## -------------------|-----------|-----------|-----------|
## (30,45.8] | 0 | 3 | 3 |
## | 0.738 | 0.241 | |
## | 0.000 | 1.000 | 0.000 |
## | 0.000 | 0.001 | |
## | 0.000 | 0.000 | |
## -------------------|-----------|-----------|-----------|
## Column Total | 1599 | 4898 | 6497 |
## | 0.246 | 0.754 | |
## -------------------|-----------|-----------|-----------|
##
## Análise:
Olahndo os intervalos de resíduos de açucar (faixas de 10 em 10), podemos ver que a maior concentração esta na faixa entre 0 e 10 (81,5%)
O mesmo comprtamento se aplica se olharmos por tipo de vinho: Brancos (75,6%) e tintos (99,3%). O que indica que os vinhos tintos tem menos açucar, pois sua concentração esta na faixa de 0 a 10 (faixa inicial) de concentração de resíduo de açucar. E os brancos apresentam maiores concetrações nas faixas superiores: Faixa de 10 a 20, Brancos (24%) x Tintos (0,7%)
attach(Vinhos)## The following objects are masked from Vinhos (pos = 3):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity## The following objects are masked from Vinhos (pos = 4):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, Vinho, volatileaciditylibrary(psych)## Warning: package 'psych' was built under R version 3.4.4describe(Vinhos)## vars n mean sd median trimmed mad min max
## fixedacidity 1 6497 7.22 1.30 7.00 7.06 0.89 3.80 15.90
## volatileacidity 2 6497 0.34 0.16 0.29 0.32 0.12 0.08 1.58
## citricacid 3 6497 0.32 0.15 0.31 0.32 0.10 0.00 1.66
## residualsugar 4 6497 5.44 4.73 3.00 4.70 2.52 0.60 45.80
## chlorides 5 6497 0.06 0.04 0.05 0.05 0.02 0.01 0.61
## freesulfurdioxide 6 6497 30.53 17.75 29.00 29.32 17.79 1.00 289.00
## totalsulfurdioxide 7 6497 115.74 56.52 118.00 115.92 57.82 6.00 440.00
## density 8 6497 0.99 0.00 0.99 0.99 0.00 0.99 1.01
## pH 9 6497 3.22 0.16 3.21 3.21 0.16 2.72 4.01
## sulphates 10 6497 0.53 0.15 0.51 0.52 0.12 0.22 2.00
## alcohol 11 6497 10.49 1.22 10.30 10.40 1.33 0.96 14.90
## quality 12 6497 5.82 0.87 6.00 5.79 1.48 3.00 9.00
## Vinho* 13 6497 1.75 0.43 2.00 1.82 0.00 1.00 2.00
## fx_redSugar* 14 6497 1.19 0.40 1.00 1.11 0.00 1.00 4.00
## range skew kurtosis se
## fixedacidity 12.10 1.72 5.05 0.02
## volatileacidity 1.50 1.49 2.82 0.00
## citricacid 1.66 0.47 2.39 0.00
## residualsugar 45.20 1.24 1.28 0.06
## chlorides 0.60 5.40 50.84 0.00
## freesulfurdioxide 288.00 1.22 7.90 0.22
## totalsulfurdioxide 434.00 0.00 -0.37 0.70
## density 0.03 0.05 -0.32 0.00
## pH 1.29 0.39 0.37 0.00
## sulphates 1.78 1.80 8.64 0.00
## alcohol 13.94 0.26 1.56 0.02
## quality 6.00 0.19 0.23 0.01
## Vinho* 1.00 -1.18 -0.61 0.01
## fx_redSugar* 3.00 1.81 2.20 0.00# describe
# A data.frame of the relevant statistics:
# item name
# item number
# number of valid cases
# mean
# standard deviation
# trimmed mean (with trim defaulting to .1)
# median (standard or interpolated
# mad: median absolute deviation (from the median)
# minimum
# maximum
# skew
# kurtosis
# standard error
summary(Vinhos)## fixedacidity volatileacidity citricacid residualsugar
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.60
## 1st Qu.: 6.400 1st Qu.:0.2300 1st Qu.:0.2500 1st Qu.: 1.80
## Median : 7.000 Median :0.2900 Median :0.3100 Median : 3.00
## Mean : 7.215 Mean :0.3397 Mean :0.3186 Mean : 5.44
## 3rd Qu.: 7.700 3rd Qu.:0.4000 3rd Qu.:0.3900 3rd Qu.: 8.10
## Max. :15.900 Max. :1.5800 Max. :1.6600 Max. :45.80
## chlorides freesulfurdioxide totalsulfurdioxide density
## Min. :0.00900 Min. : 1.00 Min. : 6.0 Min. :0.9871
## 1st Qu.:0.03800 1st Qu.: 17.00 1st Qu.: 77.0 1st Qu.:0.9923
## Median :0.04700 Median : 29.00 Median :118.0 Median :0.9949
## Mean :0.05603 Mean : 30.53 Mean :115.7 Mean :0.9947
## 3rd Qu.:0.06500 3rd Qu.: 41.00 3rd Qu.:156.0 3rd Qu.:0.9970
## Max. :0.61100 Max. :289.00 Max. :440.0 Max. :1.0140
## pH sulphates alcohol quality
## Min. :2.720 Min. :0.2200 Min. : 0.9567 Min. :3.000
## 1st Qu.:3.110 1st Qu.:0.4300 1st Qu.: 9.5000 1st Qu.:5.000
## Median :3.210 Median :0.5100 Median :10.3000 Median :6.000
## Mean :3.219 Mean :0.5313 Mean :10.4862 Mean :5.818
## 3rd Qu.:3.320 3rd Qu.:0.6000 3rd Qu.:11.3000 3rd Qu.:6.000
## Max. :4.010 Max. :2.0000 Max. :14.9000 Max. :9.000
## Vinho fx_redSugar
## RED :1599 (0,10] :5293
## WHITE:4898 (10,20] :1186
## (20,30] : 15
## (30,45.8]: 3
##
## white <- subset(Vinhos, Vinho=="WHITE", select=c(quality,fixedacidity,volatileacidity,citricacid,residualsugar,
chlorides,freesulfurdioxide,totalsulfurdioxide,density,pH,
sulphates,alcohol))Análise:
Criamos um Dataset para os vinhos Brancos, com todas as variáveis usadas anteriormente
#EstatÌsticas descritivas
summary(white)## quality fixedacidity volatileacidity citricacid
## Min. :3.000 Min. : 3.800 Min. :0.0800 Min. :0.0000
## 1st Qu.:5.000 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700
## Median :6.000 Median : 6.800 Median :0.2600 Median :0.3200
## Mean :5.878 Mean : 6.855 Mean :0.2782 Mean :0.3342
## 3rd Qu.:6.000 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900
## Max. :9.000 Max. :14.200 Max. :1.1000 Max. :1.6600
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. : 0.600 Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.: 1.700 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0
## Median : 5.200 Median :0.04300 Median : 34.00 Median :134.0
## Mean : 6.387 Mean :0.04577 Mean : 35.31 Mean :138.4
## 3rd Qu.: 9.900 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0
## Max. :45.800 Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.720 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50
## Median :0.9937 Median :3.180 Median :0.4700 Median :10.40
## Mean :0.9940 Mean :3.188 Mean :0.4898 Mean :10.51
## 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40
## Max. :1.0140 Max. :3.820 Max. :1.0800 Max. :14.20str(white)## 'data.frame': 4898 obs. of 12 variables:
## $ quality : int 5 6 6 5 7 6 5 6 6 6 ...
## $ fixedacidity : num 6.6 6.7 5.4 6.7 5.1 6.2 6.6 7.3 6.7 6.2 ...
## $ volatileacidity : num 0.24 0.34 0.18 0.3 0.26 0.22 0.25 0.27 0.26 0.12 ...
## $ citricacid : num 0.35 0.43 0.24 0.44 0.33 0.2 0.36 0.37 0.29 0.26 ...
## $ residualsugar : num 7.7 1.6 4.8 18.8 1.1 ...
## $ chlorides : num 0.031 0.041 0.041 0.057 0.027 0.035 0.045 0.042 0.038 0.044 ...
## $ freesulfurdioxide : num 36 29 30 65 46 58 54 36 40 56 ...
## $ totalsulfurdioxide: num 135 114 113 224 113 184 180 130 179 158 ...
## $ density : num 0.994 0.99 0.994 1 0.989 ...
## $ pH : num 3.19 3.23 3.42 3.11 3.35 3.11 3.08 3.48 3.23 3.52 ...
## $ sulphates : num 0.37 0.44 0.4 0.53 0.43 0.53 0.42 0.75 0.56 0.37 ...
## $ alcohol : num 10.5 12.6 9.4 9.1 11.4 9 9.2 9.9 10.4 10.5 ...Análise:
Olhando as estatísticas básicas de todas as proprieddes dos vinhos brancos, podemos perceber alguns pontos:
Médias próximas as medianas, que indica possível simetria nas distribuições para: fixedacidity, volatileacidity, citricacid, chlorides, freesulfurdioxide, totalsulfurdioxide, density, pH, sulphates, alcohol e quality.
Avaliando os valores máximos e mínimos, temos indícios de outliers para: citricacid (mínimo e máximo), residualsugar (máximo), freesulfurdioxide (máximo).
attach(white)## The following objects are masked from Vinhos (pos = 4):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 5):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 8):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity#EstatÌsticas descritivas
par (mfrow=c(3,4))
boxplot(fixedacidity, main='fixedacidity')
boxplot(volatileacidity , main='volatileacidity')
boxplot(citricacid , main='citricacid')
boxplot(residualsugar, main='residualsugar')
boxplot(chlorides, main='chlorides')
boxplot(freesulfurdioxide, main='freesulfurdioxide')
boxplot(totalsulfurdioxide, main='totalsulfurdioxide')
boxplot(density, main='density')
boxplot(pH, main='pH')
boxplot(sulphates, main='sulphates')
boxplot(alcohol, main='alcohol')
boxplot(quality, main='quality')
Análise:
Todos os Box Plots dos vinhos brancos apresentarem Outliers (exceto a variavel alcohol), que pode ser efeito dos tamanhos de amostra, os BoxPlots com maiores quantidade de outliers são: volatileacidity, citricacid, chlorides, freesulfurdioxide, citricacid e freesulfurdioxide com valores pontuais bem distantes da distribuição. Valeria uma melhor avaliação destes pontos de medidas para verificação se realmente são pontos fora da curva esperada.
Distribuições assimetricas, com principal atenção para residualsugar, onde a assimentria se destaca na forma da caixa de dos bigodes do Box Plot. Mediana deslocada para o Q1 e bigode inferior bem menor que o superior.
boxplot.stats(white$residualsugar)## $stats
## [1] 0.6 1.7 5.2 9.9 22.0
##
## $n
## [1] 4898
##
## $conf
## [1] 5.014877 5.385123
##
## $out
## [1] 26.05 31.60 22.60 45.80 31.60 26.05 23.50AIQ_residualsugar<-quantile(white$residualsugar,.75,type=2)-quantile(white$residualsugar,.25,type=2)
AIQ_residualsugar## 75%
## 8.2limsup_residualsugar= quantile(white$residualsugar,.75,type=4)+1.5*AIQ_residualsugar
limsup_residualsugar## 75%
## 22.2liminf_residualsugar= quantile(white$residualsugar,.25,type=2)-1.5*AIQ_residualsugar
liminf_residualsugar## 25%
## -10.6Análise:
Sobre as estatísticas do BoxPlot (boxplot.stat) podemos dizer: - O bigode inferiro = valor mínimo (0,6), os qurtis Q1 = 1,7 e Q2 (mediana) = 5,2 e Q3 = 9,9. O bigode superior = 22,0. Como temos valores maiores que o 22,0, teremos outliers acima de 22,0. Mostrado no $out. - Os valores do $conf, são (segundo Chambers e McGill) aproximadamente o intervalo de confiança para a mediana.
Temos também a amplitude entre quartis: Q3 - Q1 = 8,2
#excluir outliers
plot(quality~residualsugar)
white1<-subset(white, residualsugar<=22.2)
#fix(white1)Análise:
Analisando o gráfico do residuo de açucar (resildualsugar) x nota de qualidade dos vinhos brancos (quality), podemos perceber uma maior concentração de resíduos de açucar para os vinhos com notas entre 5 e 6
attach(white1)## The following objects are masked from white:
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 5):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 6):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 7):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileacidity## The following objects are masked from Vinhos (pos = 9):
##
## alcohol, chlorides, citricacid, density, fixedacidity,
## freesulfurdioxide, pH, quality, residualsugar, sulphates,
## totalsulfurdioxide, volatileaciditysummary(white1)## quality fixedacidity volatileacidity citricacid
## Min. :3.000 Min. : 3.800 Min. :0.080 Min. :0.0000
## 1st Qu.:5.000 1st Qu.: 6.300 1st Qu.:0.210 1st Qu.:0.2700
## Median :6.000 Median : 6.800 Median :0.260 Median :0.3200
## Mean :5.878 Mean : 6.854 Mean :0.278 Mean :0.3341
## 3rd Qu.:6.000 3rd Qu.: 7.300 3rd Qu.:0.320 3rd Qu.:0.3900
## Max. :9.000 Max. :14.200 Max. :1.100 Max. :1.6600
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. : 0.600 Min. :0.00900 Min. : 2.00 Min. : 9.0
## 1st Qu.: 1.700 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0
## Median : 5.200 Median :0.04300 Median : 34.00 Median :134.0
## Mean : 6.354 Mean :0.04575 Mean : 35.31 Mean :138.3
## 3rd Qu.: 9.850 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0
## Max. :22.000 Max. :0.34600 Max. :289.00 Max. :440.0
## density pH sulphates alcohol
## Min. :0.9871 Min. :2.720 Min. :0.2200 Min. : 8.00
## 1st Qu.:0.9917 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50
## Median :0.9937 Median :3.180 Median :0.4700 Median :10.40
## Mean :0.9940 Mean :3.188 Mean :0.4899 Mean :10.51
## 3rd Qu.:0.9961 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40
## Max. :1.0024 Max. :3.820 Max. :1.0800 Max. :14.20plot(residualsugar,alcohol)
abline(v=mean(residualsugar), col="red")
abline(h=mean(alcohol), col="green")
Análise:
Após tirarmos o valor de residualsugar acima de 22,2 (7 valores acima do limite do bigode do BoxPlot), podemos analisar que existe uma correlação negativa entre as variáveis, ou seja quanto maior o teor alcolico, menor a concentração de resíduo de açucar, com exceção de valores de baixo resíduo de açucar e baixa quantidade de alcool, que possivelmente pode ser explicado por não ter açucar suficiente no início do processo (suco de uva) e que não provoca uma fermentação que eleve o nível de alcool no vinho.
Ainda observando que estes valores de residuo de açucar baixo e alcool baixo, reduzem os valores de média para as duas variáveis, podendo enviezar a interpretação de uma futura análise de regressão.
# matriz de correlaÁıes
matcor <- cor(white1)
print(matcor, digits = 2)## quality fixedacidity volatileacidity citricacid
## quality 1.0000 -0.114 -0.1963 -0.0088
## fixedacidity -0.1141 1.000 -0.0248 0.2895
## volatileacidity -0.1963 -0.025 1.0000 -0.1529
## citricacid -0.0088 0.290 -0.1529 1.0000
## residualsugar -0.0995 0.087 0.0460 0.0914
## chlorides -0.2095 0.023 0.0700 0.1132
## freesulfurdioxide 0.0088 -0.049 -0.0949 0.0943
## totalsulfurdioxide -0.1746 0.091 0.0892 0.1207
## density -0.3176 0.268 0.0032 0.1483
## pH 0.0991 -0.427 -0.0334 -0.1643
## sulphates 0.0535 -0.017 -0.0379 0.0616
## alcohol 0.4363 -0.120 0.0673 -0.0765
## residualsugar chlorides freesulfurdioxide
## quality -0.100 -0.210 0.00876
## fixedacidity 0.087 0.023 -0.04884
## volatileacidity 0.046 0.070 -0.09485
## citricacid 0.091 0.113 0.09425
## residualsugar 1.000 0.086 0.30987
## chlorides 0.086 1.000 0.10095
## freesulfurdioxide 0.310 0.101 1.00000
## totalsulfurdioxide 0.408 0.199 0.61591
## density 0.831 0.261 0.30898
## pH -0.199 -0.091 0.00018
## sulphates -0.028 0.017 0.06009
## alcohol -0.462 -0.362 -0.25022
## totalsulfurdioxide density pH sulphates alcohol
## quality -0.1746 -0.3176 0.09913 0.053 0.436
## fixedacidity 0.0905 0.2682 -0.42667 -0.017 -0.120
## volatileacidity 0.0892 0.0032 -0.03342 -0.038 0.067
## citricacid 0.1207 0.1483 -0.16430 0.062 -0.077
## residualsugar 0.4081 0.8315 -0.19916 -0.028 -0.462
## chlorides 0.1990 0.2613 -0.09063 0.017 -0.362
## freesulfurdioxide 0.6159 0.3090 0.00018 0.060 -0.250
## totalsulfurdioxide 1.0000 0.5436 0.00274 0.135 -0.448
## density 0.5436 1.0000 -0.09845 0.075 -0.806
## pH 0.0027 -0.0984 1.00000 0.155 0.121
## sulphates 0.1348 0.0748 0.15517 1.000 -0.018
## alcohol -0.4484 -0.8064 0.12103 -0.018 1.000Análise:
Observando as correlações, algumas nos chamam a atenção: - residualsugar x density = 0,8315, que comprova que vinhos com muito açucar tem maior densidade, no sentido inverso; - vinhos com muito alcool tem menor densidade (correlação = -0,8064). - forte correlação entre freesulfurdioxide x totalsulfurdioxide (0,61591), devido ao livre fazer parte do total deste conservante.
#library(corrgram)
#corrgram(matcor, type = "cor", lower.panel = panel.shade, upper.panel = panel.pie)
panel.cor <- function(x, y, digits=2, prefix ="", cex.cor,
...) {
usr <- par("usr")
on.exit(par(usr))
par(usr = c(0, 1, 0, 1))
r <- cor(x, y , use = "pairwise.complete.obs")
txt <- format(c(r, 0.123456789), digits = digits) [1]
txt <- paste(prefix, txt, sep = "")
if (missing(cex.cor))
cex <- 0.8/strwidth(txt)
# abs(r) È para que na saÌda as correlaÁıes ficam proporcionais
text(0.5, 0.5, txt, cex = cex * abs(r))
}
#pdf(file = "grafico.pdf")
pairs(white1, lower.panel=panel.smooth, upper.panel=panel.cor)
Análise:
Agora podemos comprovar atraves de gráficos o que já foi comentado a análise da tabela de correlação
#avaliar inicio
dados_normalizados = as.data.frame(scale(white1))
names(dados_normalizados)## [1] "quality" "fixedacidity" "volatileacidity"
## [4] "citricacid" "residualsugar" "chlorides"
## [7] "freesulfurdioxide" "totalsulfurdioxide" "density"
## [10] "pH" "sulphates" "alcohol"summary(dados_normalizados)## quality fixedacidity volatileacidity citricacid
## Min. :-3.2482 Min. :-3.61898 Min. :-1.9740 Min. :-2.7613
## 1st Qu.:-0.9910 1st Qu.:-0.65685 1st Qu.:-0.6781 1st Qu.:-0.5299
## Median : 0.1375 Median :-0.06443 Median :-0.1797 Median :-0.1167
## Mean : 0.0000 Mean : 0.00000 Mean : 0.0000 Mean : 0.0000
## 3rd Qu.: 0.1375 3rd Qu.: 0.52800 3rd Qu.: 0.4184 3rd Qu.: 0.4617
## Max. : 3.5232 Max. : 8.70347 Max. : 8.1937 Max. :10.9572
## residualsugar chlorides freesulfurdioxide totalsulfurdioxide
## Min. :-1.1623 Min. :-1.6835 Min. :-1.95836 Min. :-3.0434
## 1st Qu.:-0.9401 1st Qu.:-0.4467 1st Qu.:-0.72367 1st Qu.:-0.7137
## Median :-0.2331 Median :-0.1261 Median :-0.07692 Median :-0.1019
## Mean : 0.0000 Mean : 0.0000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.7062 3rd Qu.: 0.1946 3rd Qu.: 0.62862 3rd Qu.: 0.6746
## Max. : 3.1604 Max. :13.7533 Max. :14.91577 Max. : 7.0987
## density pH sulphates
## Min. :-2.38090 Min. :-3.10123 Min. :-2.3651
## 1st Qu.:-0.78919 1st Qu.:-0.65126 1st Qu.:-0.7002
## Median :-0.09519 Median :-0.05532 Median :-0.1745
## Mean : 0.00000 Mean : 0.00000 Mean : 0.0000
## 3rd Qu.: 0.72311 3rd Qu.: 0.60684 3rd Qu.: 0.5265
## Max. : 2.90178 Max. : 4.18247 Max. : 5.1706
## alcohol
## Min. :-2.04414
## 1st Qu.:-0.82479
## Median :-0.09317
## Mean : 0.00000
## 3rd Qu.: 0.71973
## Max. : 2.99587describe(dados_normalizados)## vars n mean sd median trimmed mad min max range
## quality 1 4891 0 1 0.14 -0.03 1.67 -3.25 3.52 6.77
## fixedacidity 2 4891 0 1 -0.06 -0.05 0.88 -3.62 8.70 12.32
## volatileacidity 3 4891 0 1 -0.18 -0.11 0.89 -1.97 8.19 10.17
## citricacid 4 4891 0 1 -0.12 -0.07 0.74 -2.76 10.96 13.72
## residualsugar 5 4891 0 1 -0.23 -0.11 1.08 -1.16 3.16 4.32
## chlorides 6 4891 0 1 -0.13 -0.13 0.48 -1.68 13.75 15.44
## freesulfurdioxide 7 4891 0 1 -0.08 -0.06 0.96 -1.96 14.92 16.87
## totalsulfurdioxide 8 4891 0 1 -0.10 -0.03 1.01 -3.04 7.10 10.14
## density 9 4891 0 1 -0.10 -0.03 1.09 -2.38 2.90 5.28
## pH 10 4891 0 1 -0.06 -0.04 0.98 -3.10 4.18 7.28
## sulphates 11 4891 0 1 -0.17 -0.09 0.91 -2.37 5.17 7.54
## alcohol 12 4891 0 1 -0.09 -0.07 1.21 -2.04 3.00 5.04
## skew kurtosis se
## quality 0.16 0.21 0.01
## fixedacidity 0.65 2.17 0.01
## volatileacidity 1.54 4.81 0.01
## citricacid 1.28 6.18 0.01
## residualsugar 0.73 -0.52 0.01
## chlorides 5.03 37.68 0.01
## freesulfurdioxide 1.41 11.46 0.01
## totalsulfurdioxide 0.39 0.57 0.01
## density 0.25 -0.76 0.01
## pH 0.46 0.53 0.01
## sulphates 0.98 1.59 0.01
## alcohol 0.49 -0.70 0.01# componentes principais - básico
pca1 <- princomp(white1[complete.cases(white1),], cor=TRUE)
summary(pca1)## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.8376211 1.2601782 1.1725041 1.04144219 0.98963356
## Proportion of Variance 0.2814043 0.1323374 0.1145638 0.09038349 0.08161455
## Cumulative Proportion 0.2814043 0.4137417 0.5283055 0.61868901 0.70030356
## Comp.6 Comp.7 Comp.8 Comp.9
## Standard deviation 0.96393790 0.87026920 0.84619866 0.74637002
## Proportion of Variance 0.07743136 0.06311404 0.05967101 0.04642235
## Cumulative Proportion 0.77773492 0.84084896 0.90051997 0.94694232
## Comp.10 Comp.11 Comp.12
## Standard deviation 0.5812201 0.53360218 0.118928612
## Proportion of Variance 0.0281514 0.02372761 0.001178668
## Cumulative Proportion 0.9750937 0.99882133 1.000000000# componentes principais - Variáveias alta correlação
white1pca <- white1[,c(-1, -2, -3, -4, -6, -7, -8, -10, -11)]
pca2 <- princomp(white1pca[complete.cases(white1pca),], cor = TRUE)
summary(pca2)## Importance of components:
## Comp.1 Comp.2 Comp.3
## Standard deviation 1.553126 0.7335335 0.22299680
## Proportion of Variance 0.804067 0.1793571 0.01657586
## Cumulative Proportion 0.804067 0.9834241 1.00000000#### ANALISES FATORIAL Pacote PSYCH
library(psych)
pc <- principal(white1,3,rotate="varimax") #principal components
pc## Principal Components Analysis
## Call: principal(r = white1, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC3 h2 u2 com
## quality -0.34 -0.07 0.65 0.54 0.46 1.5
## fixedacidity 0.09 0.79 -0.04 0.64 0.36 1.0
## volatileacidity 0.01 -0.19 -0.59 0.38 0.62 1.2
## citricacid 0.14 0.57 0.34 0.46 0.54 1.8
## residualsugar 0.73 0.16 -0.01 0.56 0.44 1.1
## chlorides 0.36 0.05 -0.31 0.23 0.77 2.0
## freesulfurdioxide 0.61 -0.14 0.42 0.57 0.43 1.9
## totalsulfurdioxide 0.78 -0.08 0.16 0.65 0.35 1.1
## density 0.90 0.20 -0.12 0.86 0.14 1.1
## pH -0.04 -0.73 0.19 0.57 0.43 1.1
## sulphates 0.15 -0.18 0.34 0.17 0.83 1.9
## alcohol -0.79 -0.12 0.26 0.71 0.29 1.3
##
## RC1 RC2 RC3
## SS loadings 3.24 1.68 1.42
## Proportion Var 0.27 0.14 0.12
## Cumulative Var 0.27 0.41 0.53
## Proportion Explained 0.51 0.26 0.22
## Cumulative Proportion 0.51 0.78 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.11
## with the empirical chi square 7360.36 with prob < 0
##
## Fit based upon off diagonal values = 0.82?principal
str(dados_normalizados)## 'data.frame': 4891 obs. of 12 variables:
## $ quality : num -0.991 0.138 0.138 -0.991 1.266 ...
## $ fixedacidity : num -0.301 -0.183 -1.723 -0.183 -2.079 ...
## $ volatileacidity : num -0.379 0.618 -0.977 0.219 -0.18 ...
## $ citricacid : num 0.1312 0.7923 -0.7779 0.875 -0.0341 ...
## $ residualsugar : num 0.272 -0.96 -0.314 2.504 -1.061 ...
## $ chlorides : num -0.676 -0.218 -0.218 0.515 -0.859 ...
## $ freesulfurdioxide : num 0.0407 -0.3709 -0.3121 1.7457 0.6286 ...
## $ totalsulfurdioxide: num -0.0784 -0.5725 -0.5961 2.0159 -0.5961 ...
## $ density : num -0.071 -1.335 0.153 1.918 -1.57 ...
## $ pH : num 0.0109 0.2758 1.5339 -0.5188 1.0703 ...
## $ sulphates : num -1.051 -0.437 -0.788 0.351 -0.525 ...
## $ alcohol : num -0.0119 1.6952 -0.9061 -1.1499 0.7197 ...names(dados_normalizados)## [1] "quality" "fixedacidity" "volatileacidity"
## [4] "citricacid" "residualsugar" "chlorides"
## [7] "freesulfurdioxide" "totalsulfurdioxide" "density"
## [10] "pH" "sulphates" "alcohol"load=loadings(pc)
print(load,sort=TRUE,digits=3,cutoff=0.01) ##
## Loadings:
## RC1 RC2 RC3
## residualsugar 0.730 0.158 -0.011
## freesulfurdioxide 0.612 -0.142 0.422
## totalsulfurdioxide 0.784 -0.082 0.162
## density 0.896 0.201 -0.119
## alcohol -0.789 -0.122 0.262
## fixedacidity 0.085 0.794 -0.036
## citricacid 0.139 0.570 0.341
## pH -0.036 -0.733 0.186
## quality -0.340 -0.074 0.651
## volatileacidity 0.013 -0.186 -0.589
## chlorides 0.363 0.054 -0.306
## sulphates 0.148 -0.176 0.341
##
## RC1 RC2 RC3
## SS loadings 3.244 1.675 1.420
## Proportion Var 0.270 0.140 0.118
## Cumulative Var 0.270 0.410 0.528plot(load)
identify(load,labels=names(dados_normalizados)) 
## integer(0)#put names of selected points onto the figure -- to stop, click with command key
plot(pc,labels=names(dados_normalizados))
#### ANALISES FATORIAL Pacote PSYCH
library(psych)
KMO(matcor)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = matcor)
## Overall MSA = 0.36
## MSA for each item =
## quality fixedacidity volatileacidity
## 0.76 0.15 0.33
## citricacid residualsugar chlorides
## 0.74 0.30 0.67
## freesulfurdioxide totalsulfurdioxide density
## 0.59 0.68 0.40
## pH sulphates alcohol
## 0.14 0.14 0.37# componentes principais - básico
fit2 <- princomp(white1pca[complete.cases(white1pca),], cor=TRUE)
summary(fit2)## Importance of components:
## Comp.1 Comp.2 Comp.3
## Standard deviation 1.553126 0.7335335 0.22299680
## Proportion of Variance 0.804067 0.1793571 0.01657586
## Cumulative Proportion 0.804067 0.9834241 1.00000000loadings(fit2) # pc loadings##
## Loadings:
## Comp.1 Comp.2 Comp.3
## residualsugar -0.551 0.691 -0.468
## density -0.634 0.773
## alcohol 0.542 0.723 0.428
##
## Comp.1 Comp.2 Comp.3
## SS loadings 1.000 1.000 1.000
## Proportion Var 0.333 0.333 0.333
## Cumulative Var 0.333 0.667 1.000plot(fit2,type="lines", cex=1, col = "dark red") # scree plot
# the principal components
hist(fit2$scores)
biplot(fit2, cex=0.65)
library(psych)
# Escolher os componentes principais
fa.parallel (white1pca, fa="pc", show.legend=FALSE, main = "Eigenvalues dos componentes
principais")## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : A loading greater than abs(1) was detected. Examine the loadings
## carefully.## The estimated weights for the factor scores are probably incorrect. Try a different factor extraction method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate =
## rotate, : An ultra-Heywood case was detected. Examine the results carefully
## Parallel analysis suggests that the number of factors = NA and the number of components = 1# Rotação varimax
library(psych)
# Varimax Rotated Principal Components
# # extrair os fatores
vinhospca <- principal(white1pca, nfactors=1, scores=T, rotate="varimax")
vinhospca # print results ## Principal Components Analysis
## Call: principal(r = white1pca, nfactors = 1, rotate = "varimax", scores = T)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 h2 u2 com
## residualsugar 0.86 0.73 0.27 1
## density 0.98 0.97 0.03 1
## alcohol -0.84 0.71 0.29 1
##
## PC1
## SS loadings 2.41
## Proportion Var 0.80
##
## Mean item complexity = 1
## Test of the hypothesis that 1 component is sufficient.
##
## The root mean square of the residuals (RMSR) is 0.15
## with the empirical chi square 661.34 with prob < NA
##
## Fit based upon off diagonal values = 0.96fator01 = vinhospca$scores[,1]
hist(fator01)
#fator02 = vinhospca$scores[,2]
#hist(fator02)
#fator03 = vinhospca$scores[,3]
#hist(fator03)
#fator04 = vinhospca$scores[,4]
#hist(fator04)
#matriz<-cbind(white1pca,fator01)
#fix(matriz)
#attach(matriz)
#write.table(file='E:/LabBDT2018/Analise_vinhos.csv',matriz, sep=';',dec=',')